Richard Arnold Epstein

Johannes Gutenberg printed playing cards the same year as his famous Bible (1440). The cards from Gutenberg's press were Tarot cards, from which the modern deck is derived.

The Theory of Gambling and Statistical Logic (Revised Edition) 1977[edit]

In our most Puritan of society, gambling-like other pleasures-is either taxed, restricted to certain hours, or forbidden altogether. Yet the impulse to gamble remains an eternal aspect of the irrationality of man. It finds outlets in business, war, politics, in the formal overtures of the gambling casinos, and in the less ceremonious exchanges among individuals of differing opinions.

Preface To The First Edition, p. xiii

Shortly after pithecanthropus erectus gained the ascendancy, he turned his attention to the higher-order abstractions.

Chapter One, Kubeiagenesis, p. 1

"Breaking the bank at Monte Carlo" is a euphemism for closing a single gaming table. It was last accomplished at the Casino Ste. des Bains de Mer during the final days of 1957, with a harvest of 180 million francs.

Chapter One, Kubeiagenesis, p. 10

In general statistics can be considered as the offspring of the theory of probability, it builds on its parent and extends the area of patronymic jurisdiction.

Chapter Two, Mathematical Preliminaries, p. 24

A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution.

Chapter Two, Mathematical Preliminaries, p. 36

The essence of the phenomenon of gambling is decision making. The act of making a decision consists of selecting one course of action, or strategy, from among the set of admissible strategies.

Chapter Three, Fundamental Principles Of A Theory Of Gambling, p. 43

There are no conventional games involving conditions of uncertainty without risk.

Chapter Three, Fundamental Principles Of A Theory Of Gambling, p. 44

The French philosopher Pierre-Hyacinthe Azaïs (1766-1845) formalized the statement that good and evil fortune are exactly balanced in that they produce for each person an equivalent result.

Chapter Three, Fundamental Principles Of A Theory Of Gambling, p. 53

Generally, a betting system for which each wager depends only on present resources and present probability of success is known as a Markov betting system.

Chapter Three, Fundamental Principles Of A Theory Of Gambling, p. 61

Coin matching and finger flashing were among the first formal games to arise in the history of gambling. The class of Morra games extends back to the pre-Christian era, although not until comparatively recent times have game-theoretic solutions been derived.

Chapter Four, Coins, Wheels, And Oddments, p. 75

The hope of a positive expected gain lies in detecting a wheel with sufficient bias.

Against human opposition the machine usually emerges victorious, since individual patterns tend to be not random but a function of emotions and previous training and experience.

Chapter Four, Coins, Wheels, And Oddments, p. 90

While no rigorous proof of an optimal strategy has been achieved, Robbins has proposed the principal of "staying on a winner" and has shown it to be uniformly better than a strategy of random selection.

Chapter Four, Coins, Wheels, And Oddments, p. 98

The hope of a positive expected gain lies in detecting a wheel with sufficient bias.

Chapter Four, Coins, Wheels, And Oddments, p. 113

The first-known public lottery was sponsored by Augustus Caesar to raise funds for repairing the city of Rome; the first public lottery awarding money prizes, the Lotto de Firenze, was established in Florence in 1530.

Chapter Four, Coins, Wheels, And Oddments, p. 119

One of the oldest mythological fables tells of Mercury playing at dice with Selene and winning from her the five days of the epact (thus totaling the 365 days of the year and harmonizing the lunar and solar calendars).

Chapter Five, Coups And Games With Dice, p. 125

Although the major gambling casinos do not maintain statistical records on the results of games of Craps, one event has been recorded-that wherein a young man achieved 28 consecutive "passes" at the Desert Inn Casino, Las Vegas, Nevada (June 10, 1950). Odds against such an event are 400 million to 1.

Chapter Five, Coups And Games With Dice, p. 149

In 1423, the Franciscan friar St. Bernardino of Siena preached a celebrated sermon against cards (Contra Alcarum Ludos) at Bologna, attributing their invention to the devil. Despite such ecclesiastic interdiction, Johannes Gutenberg printed playing cards the same year as his famous Bible (1440). The cards from Gutenberg's press were Tarot cards, from which the modern deck is derived.

Chapter Six, The Play Of The Cards, p. 158

Reflecting an amalgam of economics, monetary, and psychological factors, the stock market represents possibly the most subtly intricate game invented by man.

Blackjack does possess a memory (the interdependence of the cards) and a conscience (inferior play will inevitably be penalized) and is not democratic (the mental agility and retentiveness of the player are significant factors).

Chapter Seven, Blackjack, p. 215

Because the fluctuations in the composition of the deck as it is dependent over successive (and dependent) trials, it is intuitively apparent that altering decisions or the magnitude of the wager or both in accordance with the fluctuations should prove advantageous to the player.

Chapter Seven, Blackjack, p. 231

Contract Bridge is likely the most challenging card game extant; it is certainly the the most obsessive for its ranks of zealous followers. The initial progenitor of all Bridge forms is the game of Triumph, which gained currency about A.D. 1500. In the mid seventeenth century, Triumph evolved into Whist, a partnership game for four players. The change from Whist to Bridge occurred about 1886with a publication in London of a small pamphlet, titled Biritch or Russian Whist.

Chapter Eight, Contract Bridge, p. 252

The earliest full-length account of a chariot race appears in Book xxiii of the Iliad.

Treatment of the apparently whimsical fluctuations of the stock quotations as truly non stationary processes requires a model of such complexity that its practical value is likely to be limited. An additional complication, not encompassed by most stock market models, arises from the manifestation of the market as a nonzero sum game.

A weakness of the random-walk model lies in its assumption of instantaneous adjustment, whereas the information impelling a stock market toward its "intrinsic value" gradually becomes disseminated throughout the market place.

The earliest full-length account of a chariot race appears in Book xxiii of the Iliad.

From a rational standpoint, it might be expected that man should be far more willing to express financial confidence in his skills rather than risking his earnings on the mindless meanderings of chance. Experience, however, has strongly indicated the reverse proposition to hold true.

Chapter Ten, Games Of Pure Skill And Competitive Computers, p. 337

Anthropologists have often commented on the striking resemblance between the uneducated gambler and the primitive.

Chapter Eleven, Fallacies And Sophistries, p. 391

The assumption that individuals act objectively in accordance with purely mathematical dictates to maximize their gain or utility cannot be sustained by empirical observation.